相关论文: An hp-Adaptive Sampling Algorithm for Dispersion R…
Dispersion relations govern wave behaviors, and tailoring them is a grand challenge in wave manipulation. We demonstrate inverse design of phononic dispersion using non-local interactions on one-dimensional spring-mass chains. For both…
This paper presents a point-wise divergence-free projection method for numerical approximations of photonic quasicrystals problems. The original three-dimensional quasiperiodic Maxwell's system is transformed into a periodic one in higher…
In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on…
We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic…
Learned image compression methods have shown superior rate-distortion performance and remarkable potential compared to traditional compression methods. Most existing learned approaches use stacked convolution or window-based self-attention…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…
In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small…
In this paper we consider functions in the Hardy space $\mathbf{H}_2^{p\times q}$ defined in the unit disc of matrix-valued. We show that it is possible, as in the scalar case, to decompose those functions as linear combinations of suitably…
We present an algorithm for solving the radiative transfer problem on massively parallel computers using adaptive mesh refinement and domain decomposition. The solver is based on the method of characteristics which requires an adaptive…
By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic…
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values…
We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…
We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem --…
A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in…
We consider the standard adaptive finite element loop SOLVE, ESTIMATE, MARK, REFINE, with ESTIMATE being implemented using the $p$-robust equilibrated flux estimator, and MARK being D\"orfler marking. As a refinement strategy we employ…
Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in…
A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta…